CN111879842B - Coordinate mapping method for different dimension spaces and single cell mass spectrum detection method - Google Patents
Coordinate mapping method for different dimension spaces and single cell mass spectrum detection method Download PDFInfo
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Abstract
The invention provides a coordinate mapping method of different dimension spaces, which comprises the following steps: (A1) establishing two-dimensional and three-dimensional coordinate systems respectively; (A2) selecting a plurality of mapping points in a two-dimensional coordinate system; (A3) Moving in a three-dimensional coordinate system, so that the position in the three-dimensional coordinate system corresponds to the mapping point when being reflected in a two-dimensional coordinate system, and acquiring a three-dimensional coordinate point corresponding to the two-dimensional coordinate point of the mapping point; (A4) By utilizing the three-dimensional coordinate points and the two-dimensional coordinate points, an EIV adjustment model of cross-dimension conversion is constructed: (A5) And solving the EIV adjustment model to obtain an initial coordinate mapping matrix. The invention has the advantages of high precision and the like.
Description
Technical Field
The invention relates to the field of biological detection, in particular to a coordinate mapping method of different dimensional spaces and application of the coordinate mapping method in single-cell mass spectrometry detection.
Background
Cells are the basic units that make up life bodies, and methods for single cell analysis are needed to understand the changes and behavior of individual cells at various stages in a complex and diverse environment. The mass spectrum is a multi-component simultaneous analysis method, according to the molecular weight difference of various components in the cells, the mass spectrum can form spectrum peaks arranged according to mass numbers in the mass spectrum, and the molecular information of the various components in the cells can be obtained through multi-stage mass spectrum analysis. Because the mass spectrometry does not need to be marked and the information of the molecules to be detected does not need to be known in advance, various unknown components in the cells can be rapidly identified, and the histology information of proteins and even small molecule metabolites in the cells can be obtained. In addition, the mass spectrum can easily obtain the isotope information of each component molecule, and the accurate quantification of various molecules to be detected in cells can be realized by adopting an isotope internal standard and dilution technology. Mass spectrometry single cell analysis has therefore recently received high attention and is believed to play an important role in the study of single cell histology.
The single-cell mass spectrum is used for controlling the capillary needle to obtain effective substances through the micro-operation system by means of a microscope, and then the effective substances in the capillary needle are sent into the mass spectrometer by utilizing high-voltage electricity, so that required data are obtained.
The cell diameter is micron or submicron, so the precision requirement on the micro-operation system is high. The system coordinate mapping is a precondition for ensuring the precision of the microscopic operation.
Coordinate transformation is commonly used in the fields of geodetic, photogrammetry, map projection, computer vision, robotics, micro-operations, and the like. The existing micro-operation processing mode is used as a linear system, namely, errors are not considered, and measured data are directly solved. However, the system is an optical-mechanical-electrical strong coupling system, and is not a linear system, and the coordinate conversion process is affected by errors in various aspects such as structure, light path, installation and measurement. Therefore, the existing coordinate conversion has larger error, and correspondingly, the precision of micro-operation is reduced.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a high-precision and low-error coordinate mapping method for different dimensional spaces.
The invention aims at realizing the following technical scheme:
the coordinate mapping method of the different dimension space comprises the following steps:
(A1) Respectively establishing a two-dimensional coordinate system and a three-dimensional coordinate system;
(A2) Selecting a plurality of mapping points in a two-dimensional coordinate system;
(A3) Moving in a three-dimensional coordinate system, so that the position in the three-dimensional coordinate system corresponds to the mapping point when being reflected in a two-dimensional coordinate system, and acquiring a three-dimensional coordinate point corresponding to the two-dimensional coordinate point of the mapping point;
(A4) By utilizing the three-dimensional coordinate points and the two-dimensional coordinate points, an EIV (electronic interference vector) adjustment model of cross-dimension conversion is constructed:
n is the number of coordinates, i is a natural number, and i is not more than n; (x) si ,y si ) Is a two-dimensional coordinate point, (x) mi ,y mi ,z mi ) Is a three-dimensional coordinate point; e, e xsi ,e ysi 2n×1 random error vector, e, as two-dimensional coordinates xmi ,e ymi ,e zmi 2n x 1 random error vectors for three-dimensional coordinates; e represents an n×1 vector of all 1's; r is a rotation matrix;is a translation matrix; i n Representing a three-dimensional identity matrix; delta x ,Δ y ,Δ z Feedforward delta in three dimensions, respectively, associated with the applied system; q=q+q i ·i+q 2 ·j+q 3 ·k，q 0 Is the rotation angle value, (q) 1 ,q 2 ,q 3 ) Is a three-dimensional axis vector; q 0 ,q 1 ,q 2 ,q 3 Is real, i 2 ＝j 2 ＝k 2 ＝1；
(A5) And solving the EIV adjustment model to obtain an initial coordinate mapping matrix.
The invention also aims to provide a single-cell mass spectrum detection method applying the coordinate mapping method, and the aim of the invention is realized by the following technical scheme:
according to the single-cell mass spectrum detection method of the coordinate mapping method of the different dimension spaces, the three-dimensional coordinate system is built based on the movement of the three-dimensional mechanical arm, and the two-dimensional coordinate system is built based on the control screen; the capillary needle is arranged on the three-dimensional mechanical arm
Compared with the prior art, the invention has the following beneficial effects:
1. the precision is high;
a nonlinear compensation algorithm is constructed: the three-dimensional to two-dimensional conversion matrix is converted, feedforward is introduced based on the reduction of nonlinear errors, the precision of coordinate mapping is improved, and the precision of three-dimensional micro-operation in specific application is correspondingly improved, so that the automation efficiency of single-cell mass spectrum detection is remarkably improved;
the EIV adjustment model is converted into the GH model, so that the precision and the efficiency of matrix solving are improved;
the problem that the mechanical arm is three-dimensional and the screen is two-dimensional and cannot be converted is solved;
2. the error is small;
the conversion matrix based on the optimization algorithm is designed by using the method of measuring the adjustment, so that the influence caused by random errors is reduced;
an automatic optimized conversion matrix method is constructed in the process of three-dimensional movement, and the problem of overlarge system error is solved.
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The present disclosure will become more readily understood with reference to the accompanying drawings. As will be readily appreciated by those skilled in the art: the drawings are only for illustrating the technical scheme of the present invention and are not intended to limit the scope of the present invention. In the figure:
FIG. 1 is a flow chart of a coordinate mapping method for different dimensional spaces according to an embodiment of the invention.
Detailed Description
Fig. 1 and the following description depict alternative embodiments of the invention to teach those skilled in the art how to make and reproduce the invention. In order to teach the technical solution of the present invention, some conventional aspects have been simplified or omitted. Those skilled in the art will appreciate variations or alternatives derived from these embodiments that fall within the scope of the invention. Those skilled in the art will appreciate that the features described below can be combined in various ways to form multiple variations of the invention. Thus, the invention is not limited to the following alternative embodiments, but only by the claims and their equivalents.
Example 1:
fig. 1 schematically shows a flowchart of a coordinate mapping method of a different dimensional space according to embodiment 1 of the present invention, as shown in fig. 1, the coordinate mapping method of a different dimensional space includes the following steps:
(A1) Respectively establishing a two-dimensional coordinate system and a three-dimensional coordinate system;
(A2) Selecting a plurality of mapping points in a two-dimensional coordinate system;
(A3) Moving in the three-dimensional coordinate system, so that the position in the three-dimensional coordinate system corresponds to the mapping point when being reflected (e.g. imaged by a camera) in the two-dimensional coordinate system (e.g. a screen for displaying imaging), and acquiring three-dimensional coordinate points corresponding to the two-dimensional coordinate points of the mapping point, namely acquiring two-dimensional coordinate points and three-dimensional coordinate points with a plurality of one-to-one correspondence systems;
(A4) By utilizing the three-dimensional coordinate points and the two-dimensional coordinate points, an EIV (electronic interference vector) adjustment model of cross-dimension conversion is constructed:
n is the number of coordinates, i is a natural number, and i is not more than n; (x) si ,y si ) Is a two-dimensional coordinate point, (x) mi ,y mi ,z mi ) Is a three-dimensional coordinate point; e, e xsi ,e ysi 2n×1 random error vector, e, as two-dimensional coordinates xmi ,e ymi ,e zmi In three dimensions2n x 1 random error vectors; e represents an n×1 vector of all 1's; r is a rotation matrix;is a translation matrix; i n Representing a three-dimensional identity matrix; delta x ,Δ y ,Δ z Feedforward delta in three dimensions, respectively, associated with the applied system; q=q+q i ·i+q 2 ·j+q 3 ·k，q 0 Is the rotation angle value, (q) 1 ,q 2 ,q 3 ) Is a three-dimensional axis vector; q 0 ,q 1 ,q 2 ,q 3 Is real, i 2 ＝j 2 ＝k 2 ＝1；
(A5) And solving the EIV adjustment model to obtain an initial coordinate mapping matrix.
In order to reduce nonlinear errors and improve solving efficiency, further, feed forward delta is fitted to a first, second or third order polynomial.
In order to obtain feedforward efficiently, further, the feedforward fitting is performed in the following manner:
acquiring actual coordinate displacement at each interval distance, repeating for at least three times, subtracting the actual coordinate displacement from theoretical coordinate displacement, and acquiring feedforward coordinates of each dimension; the spacing distance is 10 μm-100 μm;
obtaining at least three fitting point curves of each dimension by utilizing the feedforward coordinates;
at least three fitting point curves for each dimension are fitted to a fitted curve.
In order to solve efficiently and with high precision, in step (A5), the solution is as follows:
converting the EIV adjustment model into a GH model:
setting the parameter to be estimated to be ζ= [ T ] x T y q 0 q 1 q 2 q 3 ] T Nonlinear micro-conditions and the likeThe formula is:
wherein: i=1, 2..n; j=1, 2; s= [ x ] s1 y s1 … x sn y sn ] T ；
M＝[x m1 y m1 … x mn y mn ] T 。
In order to improve the coordinate mapping precision, further, the selection criteria of the mapping points are:
the mapping points are not less than 9 and uniformly distributed in the two-dimensional coordinate system.
In order to further improve the coordinate conversion accuracy, the coordinate mapping method further includes the steps of:
(A6) Obtaining a current coordinate and a target coordinate in a two-dimensional coordinate system (such as a computer screen for displaying imaging) corresponding to real-time movement in a three-dimensional space, and selecting an optimized mapping point in a range including the current coordinate and the target coordinate in the two-dimensional coordinate system;
(A7) And (3) obtaining an optimized coordinate mapping matrix by utilizing the optimized mapping points and executing the steps (A3) - (A4).
In order to improve the accuracy of the optimized coordinate mapping, further, the range is: circles with current coordinates and target coordinates as diameters.
In order to further improve the accuracy of the optimized coordinate mapping, further, the optimized mapping points are mapping points in the step (A2) within the range;
and if the mapping points in the step (A2) do not exist in the range, selecting the mapping points in at least two steps (A2) closest to the current coordinates and the target coordinates.
Example 2:
an application example of the coordinate mapping method of different dimensional spaces according to the embodiment 1 of the invention in single cell mass spectrometry detection.
The single-cell mass spectrum detection method of the application example comprises the following steps:
(A1) Establishing the three-dimensional coordinate system (x m ,y m ,z m ): the z-axis coordinate corresponds to the focal plane of the microscope, and the position of the end part of the capillary needle is in the same plane with the focal plane of the microscope; the capillary needle is arranged on the three-dimensional mechanical arm;
two-dimensional coordinate system (x) is established based on computer screen s ,y s ) The method comprises the steps of carrying out a first treatment on the surface of the Imaging the end part of the capillary needle by using a camera and displaying the end part on a computer screen;
(A2) Preferably 9 mapping points, uniformly tiling the entire screen in a3×3 array pattern;
(A3) Moving the capillary needle to a preferred position by utilizing a three-dimensional mechanical arm, and recording coordinate points of the mechanical arm, so that one-to-one correspondence between screen coordinates and three-dimensional mechanical arm coordinates is obtained, and correspondence among 9 groups of coordinate points is obtained;
(A4) By utilizing the three-dimensional coordinate points and the two-dimensional coordinate points, an EIV (electronic interference vector) adjustment model of cross-dimension conversion is constructed:
n is the number of coordinates, i is a natural number, and i is not more than n; (x) si ,y si ) Is a two-dimensional coordinate point, (x) mi ,y mi ,z mi ) Is a three-dimensional coordinate point; e, e xsi ,e ysi 2n×1 random error vector, e, as two-dimensional coordinates xmi ,e ymi ,e zmi 2n x 1 random error vectors for three-dimensional coordinates; e represents an n×1 vector of all 1's; r is a rotation matrix;is a translation matrix; i n Representing a three-dimensional identity matrix; delta x ,Δ y ,Δ z Feedforward delta in three dimensions, respectively, associated with the applied system; q＝q+q i ·i+q 2 ·j+q 3 ·k，q 0 Is the rotation angle value, (q) 1 ,q 2 ,q 3 ) Is a three-dimensional axis vector; q 0 ,q 1 ,q 2 ,q 3 Is real, i 2 ＝j 2 ＝k 2 ＝1；
The EIV adjustment model considers the nonlinear errors of a motor and a reduction gearbox in a single-cell mass spectrum detection system, and the feedforward delta is added according to the applied system, so that the feedforward delta can be fitted into first-order, second-order and third-order polynomials in the specific mode that:
the tip of the capillary needle obtains actual coordinate displacement every interval distance, the actual coordinate displacement is repeated for at least three times, and the actual coordinate displacement is subtracted from the theoretical coordinate displacement to obtain feedforward coordinates of each dimension; the spacing distance is 10 μm-100 μm;
obtaining at least three fitting point curves of each dimension by utilizing the feedforward coordinates; fitting at least three fitting point curves of each dimension into a fitting curve;
in this embodiment, the feedforward is fitted to a second order polynomial (i.e., three dimensions, all using the polynomial):
Δ＝ax+bx 2 +c；
wherein: a. b and c are constants, and in the embodiment, 0.03, 0.005 and 0.07 are obtained through experiments and fitting respectively;
(A5) Converting the EIV model to a GH model:
setting the parameter to be estimated to be ζ= [ T ] x T y q 0 q 1 q 2 q 3 ] T Its nonlinear micro-conditional equation is:
wherein: i=1, 2..n;
j＝1,2；
S＝[x s1 y s1 … x sn y sn ] T ；
M＝[x m1 y m1 z m1 … x mn y mn z mn ] T 。
linearization is as follows:
the first order bias guide is as follows:
the closure difference is:
then xi can be calculated by i+1 ：
Wherein the normal matrix N is:
a lambda Lagrangian multiplier;represented by lambda i+1 Is a function of the estimated value of (2);
residual vectorCan be expressed as:
from the above solutionAs initial value for the next iteration, untilEpsilon is an iteration threshold;
the initial mapping matrix can be solved;
(A6) The method comprises the steps of obtaining the current coordinates and target coordinate points of a capillary needle point on a computer screen (a two-dimensional coordinate system), and selecting an optimized mapping point in a range comprising the current coordinates and the target coordinates in the two-dimensional coordinate system, wherein the optimized mapping point comprises the following specific steps:
making a circle by taking the current coordinate and the target coordinate as diameters, wherein the optimized mapping points are mapping points in the step (A2) in the circle; if the mapping points in the step (A2) do not exist in the range, selecting at least two mapping points in the step (A2) closest to the current coordinate and the target coordinate, and optimizing the number of the mapping points to be not more than 9;
(A7) Obtaining an optimized coordinate mapping matrix by using the optimized mapping points and executing the steps (A3) - (A4);
the steps (A6) - (A7) should be completed before each step of action of the capillary needle, namely, a new mapping point must be obtained for each step of action, so that a new coordinate mapping matrix with higher precision is obtained, and the problem of overlarge system error is solved.
To verify the effectiveness of the method, two sets of comparative experiments were performed:
comparative example 1:
in the conventional linear coordinate mapping method in single-cell mass spectrometry, coordinate points covering the whole screen are selected for experimental verification, and partial comparison results are shown in the following table:
table 1 linear algorithm vs. present method test data:
from the comparison result, the accuracy of the method is 8 times that of the linear algorithm.
Comparative example 2:
the difference between the coordinate mapping method without feedforward based on the EIV model and the coordinate mapping method without feedforward based on the EIV model is that feedforward in the EIV model is removed. And selecting coordinate points covering the whole screen for experimental verification, wherein partial comparison results are shown in the following table:
table 2 linear algorithm vs. present method test data:
from the comparison result, the accuracy of the algorithm is more than 3 times of that of the linear algorithm.
The above embodiment gives a feed forward fit by way of example only: the three dimensions use the same polynomial, but may also be fitted separately in the three dimensions in the same manner as in example 2.
Claims (10)
1. A coordinate mapping method of different dimensional spaces, the coordinate mapping method of different dimensional spaces comprising the steps of:
(A1) Respectively establishing a two-dimensional coordinate system and a three-dimensional coordinate system;
(A2) Selecting a plurality of mapping points in a two-dimensional coordinate system;
(A3) Moving in a three-dimensional coordinate system, so that the position in the three-dimensional coordinate system corresponds to the mapping point when being reflected in a two-dimensional coordinate system, and acquiring a three-dimensional coordinate point corresponding to the two-dimensional coordinate point of the mapping point;
(A4) By utilizing the three-dimensional coordinate points and the two-dimensional coordinate points, an EIV adjustment model of cross-dimension conversion is constructed:
n is the number of coordinates, i is a natural number, and i is not more than n; (x) si ,y si ) Is a two-dimensional coordinate point, (x) mi ,y mi ,z mi ) Is a three-dimensional coordinate point; e, e xsi ,e ysi 2n×1 random error vector, e, as two-dimensional coordinates xmi ,e ymi ,e zmi 2n x 1 random error vectors for three-dimensional coordinates; e represents an n×1 vector of all 1's; r is a rotation matrix;is a translation matrix; i n Representing a three-dimensional identity matrix; delta x ,Δ y ,Δ z Feedforward delta in three dimensions, respectively, associated with the applied system; q=q 0 +q 1 ·i+q 2 ·j+q 3 ·k，q 0 Is the rotation angle value, (q) 1 ,q 2 ,q 3 ) Is a three-dimensional axis vector; q 0 ,q 1 ,q 2 ,q 3 Is real, i 2 ＝j 2 ＝k 2 ＝1；
(A5) And solving the EIV adjustment model to obtain an initial coordinate mapping matrix.
2. The coordinate mapping method of different dimensional space according to claim 1, wherein: the feed forward delta fit is a first, second or third order polynomial.
3. The coordinate mapping method of different dimensional space according to claim 2, wherein: the feed forward delta fitting mode is as follows:
acquiring actual coordinate displacement at each interval distance, repeating for at least three times, subtracting the actual coordinate displacement from theoretical coordinate displacement, and acquiring feedforward coordinates of each dimension; the spacing distance is 10 μm-100 μm;
obtaining at least three fitting point curves of each dimension by utilizing the feedforward coordinates;
at least three fitting point curves for each dimension are fitted to a fitted curve.
4. The coordinate mapping method of different dimensional space according to claim 1, wherein: in the step (A5), the solution is as follows:
converting the EIV adjustment model into a GH model:
setting the parameter to be estimated to be ζ= [ T ] x T y q 0 q 1 q 2 q 3 ] T Its nonlinear micro-conditional equation is:
wherein: i=1, 2..n; j=1, 2; s= [ x ] s1 y s1 … x sn y sn ] T ；
M＝[x m1 y m1 … x mn y mn ] T 。
5. The coordinate mapping method of different dimensional space according to claim 1, wherein: the selection criteria of the mapping points are:
the mapping points are not less than 9 and uniformly distributed in the two-dimensional coordinate system.
6. The coordinate mapping method of different dimensional space according to claim 1, wherein: the coordinate mapping method further comprises the steps of:
(A6) Obtaining a current coordinate and a target coordinate in a two-dimensional coordinate system corresponding to real-time movement in a three-dimensional space, and selecting an optimal mapping point in a range including the current coordinate and the target coordinate in the two-dimensional coordinate system;
(A7) And (3) obtaining an optimized coordinate mapping matrix by utilizing the optimized mapping points and executing the steps (A3) - (A4).
7. The coordinate mapping method of different dimensional space according to claim 6, wherein: the range is as follows: circles with current coordinates and target coordinates as diameters.
8. The coordinate mapping method of different dimensional space according to claim 6, wherein:
the optimized mapping points are mapping points in step (A2) within the range;
and if the mapping points in the step (A2) do not exist in the range, selecting the mapping points in at least two steps (A2) closest to the current coordinates and the target coordinates.
9. The single-cell mass spectrum detection method of the coordinate mapping method of different dimension spaces according to any one of claims 1-8, wherein the three-dimensional coordinate system is established based on the movement of a three-dimensional mechanical arm, and the two-dimensional coordinate system is established based on a control screen; the capillary needle is arranged on the three-dimensional mechanical arm.
10. The single cell mass spectrometry detection method of claim 9, wherein: in the three-dimensional coordinate system, the z-axis coordinate corresponds to the focal plane of the microscope, and the position of the end part of the capillary needle is in the same plane with the focal plane of the microscope.
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